こんにちは！
ご質問ありがとうございます。
ご質問について、ここで言う『[経済](https://eikaiwa.dmm.com/uknow/questions/98507/)の循環』は、economic stimulation が近い表現かと思います。
以下のように質問にある内容を説明できます。
Hosting international sports events can increase employment and inbound effects, leading to new job opportunities and an economic boost. As the economy gains momentum, businesses are more inclined to hire people. This positive cycle ensures that those involved in the sports events can keep stable employment even after the events.
参考になれば幸いです。
日本 
